Taxonomy for Mathematics Articles-11th Class: Difference between revisions
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{| class="wikitable" | {| class="wikitable" | ||
!S.No | !S.No | ||
!Chapters | !Chapters | ||
!Topics | |||
!'''Article Creator Name''' | |||
!'''अध्याय''' | !'''अध्याय''' | ||
!विषय | !विषय | ||
Line 9: | Line 10: | ||
|Sets | |Sets | ||
|Sets and their representations | |Sets and their representations | ||
|Ramamurthy | |||
Mani | |||
|समुच्चय | |समुच्चय | ||
|समुच्चय और उनका निरूपण | |[[समुच्चय और उनका निरूपण]] | ||
|- | |- | ||
| | | | ||
| | | | ||
|The Empty Set | |The Empty Set/Void Set | ||
|Ramamurthy | |||
Mani | |||
| | | | ||
|रिक्त समुच्चय | |[[रिक्त समुच्चय]] | ||
|- | |- | ||
| | | | ||
| | | | ||
|Finite and Infinite Sets | |Finite and Infinite Sets | ||
|Ramamurthy | |||
Mani | |||
| | | | ||
|परिमित और अपरिमित समुच्चय | |[[परिमित और अपरिमित समुच्चय]] | ||
|- | |- | ||
| | | | ||
| | | | ||
|Equal Sets | |Equal Sets | ||
|Ramamurthy | |||
Mani | |||
| | | | ||
|समान समुच्चय | |[[समान समुच्चय]] | ||
|- | |- | ||
| | | | ||
Line 34: | Line 43: | ||
|Subsets | |Subsets | ||
| | | | ||
|उपसमुच्चय | | | ||
|[[उपसमुच्चय]] | |||
|- | |- | ||
| | | | ||
| | | | ||
|Power Set | |Power Set | ||
|Ramamurthy | |||
Mani | |||
| | | | ||
|घात समुच्चय | |[[घात समुच्चय]] | ||
|- | |- | ||
| | | | ||
| | | | ||
|Universal Set | |Universal Set | ||
|Ramamurthy | |||
Mani | |||
| | | | ||
|सार्वत्रिक समुच्चय | |[[सार्वत्रिक समुच्चय]] | ||
|- | |- | ||
| | | | ||
| | | | ||
|Venn Diagrams | |Venn Diagrams | ||
|Ramamurthy | |||
Mani | |||
| | | | ||
|वेन आरेख | |[[वेन आरेख]] | ||
|- | |- | ||
| | | | ||
| | | | ||
|Operations on Sets | |Operations on Sets | ||
|Ramamurthy | |||
Mani | |||
| | | | ||
|समुच्चयों पर संक्रियाएँ | |[[समुच्चयों पर संक्रियाएँ]] | ||
|- | |- | ||
| | | | ||
Line 64: | Line 82: | ||
|Complement of a Set | |Complement of a Set | ||
| | | | ||
|समुच्चय का पूरक | | | ||
|[[समुच्चय का पूरक]] | |||
|- | |- | ||
| | | | ||
Line 70: | Line 89: | ||
|Practical Problems on Union and Intersection of Two Sets | |Practical Problems on Union and Intersection of Two Sets | ||
| | | | ||
|दो समुच्चयों के सम्मिलन और सर्वनिष्ठ पर आधारित व्यावहारिक प्रश्न | | | ||
|[[दो समुच्चयों के सम्मिलन और सर्वनिष्ठ पर आधारित व्यावहारिक प्रश्न]] | |||
|- | |||
| | |||
| | |||
|Sets | |||
| | |||
| | |||
|[[समुच्चय]] | |||
|- | |||
| | |||
| | |||
|Geometry | |||
| | |||
| | |||
|[[ज्यामिति]] | |||
|- | |||
| | |||
| | |||
|Sequences | |||
| | |||
| | |||
|[[अनुक्रम]] | |||
|- | |||
| | |||
| | |||
|Probability | |||
| | |||
| | |||
|[[प्रायिकता]] | |||
|- | |||
| | |||
| | |||
|Trigonometric series | |||
| | |||
| | |||
|[[त्रिकोणमितीय श्रेणी]] | |||
|- | |||
| | |||
| | |||
|Natural Numbers | |||
| | |||
| | |||
|[[प्राकृत संख्याएँ]] | |||
|- | |||
| | |||
| | |||
|Prime Numbers | |||
| | |||
| | |||
|[[अभाज्य संख्याएँ]] | |||
|- | |||
| | |||
| | |||
|Triangles | |||
| | |||
| | |||
|[[त्रिभुज]] | |||
|- | |||
| | |||
| | |||
|Prime factors | |||
| | |||
| | |||
|[[अभाज्य गुणनखंड]] | |||
|- | |||
| | |||
| | |||
|Equation | |||
| | |||
| | |||
|[[समीकरण]] | |||
|- | |||
| | |||
| | |||
|Integers | |||
| | |||
| | |||
|[[पूर्णांक]] | |||
|- | |||
| | |||
| | |||
|Rational Numbers | |||
| | |||
| | |||
|[[परिमेय संख्याएँ]] | |||
|- | |||
| | |||
| | |||
|Real Numbers | |||
| | |||
| | |||
|[[वास्तविक संख्याएँ]] | |||
|- | |||
| | |||
| | |||
|Roster or tabular form (Sets) | |||
| | |||
| | |||
|[[रोस्टर या सारणीबद्ध रूप (समुच्चय)]] | |||
|- | |||
| | |||
| | |||
|Set-builder form (Sets) | |||
| | |||
| | |||
|[[समुच्चय-निर्माण रूप(समुच्चय)]] | |||
|- | |||
| | |||
| | |||
|Null Set | |||
| | |||
| | |||
|[[शून्य समुच्चय]] | |||
|- | |||
| | |||
| | |||
|Superset | |||
| | |||
| | |||
|[[अधिसमुच्चय]] | |||
|- | |||
| | |||
| | |||
|Singleton set | |||
| | |||
| | |||
|[[एकल समुच्चय]] | |||
|- | |||
| | |||
| | |||
|Closed Interval | |||
| | |||
| | |||
|[[संवृत(बंद) अंतराल]] | |||
|- | |||
| | |||
| | |||
|Open Interval | |||
| | |||
| | |||
|[[खुला अंतराल]] | |||
|- | |||
| | |||
| | |||
|Union (sets) | |||
| | |||
| | |||
|[[सम्मिलन(समुच्चय)]] | |||
|- | |||
| | |||
| | |||
|Intersection (sets) | |||
| | |||
| | |||
|[[सर्वनिष्ट(समुच्चय)]] | |||
|- | |- | ||
| | |||
| | |||
|Disjoint Sets | |||
| | |||
| | |||
|[[असंयुक्त समुच्चय]] | |||
|- | |||
| | |||
| | | | ||
| | | | ||
Line 81: | Line 263: | ||
|Relations and Functions | |Relations and Functions | ||
|Cartesian Product of Sets | |Cartesian Product of Sets | ||
| | |||
|संबंध और फलन | |संबंध और फलन | ||
|समुच्चयों का कार्टेशियन गुणन | |[[समुच्चयों का कार्टेशियन गुणन]] | ||
|- | |- | ||
| | | | ||
Line 88: | Line 271: | ||
|Relations | |Relations | ||
| | | | ||
|संबंध | | | ||
|[[संबंध]] | |||
|- | |- | ||
| | | | ||
Line 94: | Line 278: | ||
|Functions | |Functions | ||
| | | | ||
|फलन | | | ||
|[[फलन]] | |||
|- | |||
| | |||
| | |||
|Ordered triplet | |||
| | |||
| | |||
|[[क्रमित त्रिक]] | |||
|- | |||
| | |||
| | |||
|Domain (sets) | |||
| | |||
| | |||
|[[प्रांत(समुच्चय)]] | |||
|- | |||
| | |||
| | |||
|Range (Sets) | |||
| | |||
| | |||
|[[परिसर(समुच्चय)]] | |||
|- | |||
| | |||
| | |||
|Arrow diagram (Sets) | |||
| | |||
| | |||
|[[दृष्टि चित्रण(समुच्चय)]] | |||
|- | |||
| | |||
| | |||
|Codomain (Sets) | |||
| | |||
| | |||
|[[सहप्रांत(समुच्चय)]] | |||
|- | |||
| | |||
| | |||
|Real Function | |||
| | |||
| | |||
|[[वास्तविक फलन]] | |||
|- | |||
| | |||
| | |||
|Identity function (sets) | |||
| | |||
| | |||
|[[तत्समक फलन(समुच्चय)]] | |||
|- | |||
| | |||
| | |||
|Constant function (sets) | |||
| | |||
| | |||
|[[अचर फलन(समुच्चय)]] | |||
|- | |||
| | |||
| | |||
|Polynomial functions (sets) | |||
| | |||
| | |||
|[[बहुपदीय फलन(समुच्चय)]] | |||
|- | |- | ||
| | |||
| | |||
|Rational functions (sets) | |||
| | |||
| | |||
|[[परिमेय फलन(समुच्चय)]] | |||
|- | |||
| | |||
| | |||
|Modulus function (sets) | |||
| | |||
| | |||
|[[मापांक फलन(समुच्चय)]] | |||
|- | |||
| | |||
| | |||
|Signum function (sets) | |||
| | |||
| | |||
|[[चिन्ह फलन(समुच्चय)]] | |||
|- | |||
| | |||
| | |||
|Greatest integer function (sets) | |||
| | |||
| | |||
|[[महत्तम पूर्णांक फलन(समुच्चय)]] | |||
|- | |||
| | |||
| | | | ||
| | | | ||
Line 105: | Line 382: | ||
|Trignometric Functions | |Trignometric Functions | ||
|Angles | |Angles | ||
|Ramamurthy | |||
Mani | |||
|त्रिकोणमितीय फलन | |त्रिकोणमितीय फलन | ||
|कोण | |[[कोण]] | ||
|- | |||
| | |||
| | |||
|Trigonometric Functions | |||
| | |||
| | |||
|[[त्रिकोणमितीय फलन]] | |||
|- | |||
| | |||
| | |||
|Trigonometric Functions of Sum and Difference of Two Angles | |||
| | |||
| | |||
|[[दो कोणों के योग और अंतर का त्रिकोणमितीय फलन]] | |||
|- | |||
| | |||
| | |||
|Trigonometric Equations | |||
| | |||
| | |||
|[[त्रिकोणमितीय समीकरण]] | |||
|- | |||
| | |||
| | |||
|Trigonometry | |||
| | |||
| | |||
|[[त्रिकोणमिति]] | |||
|- | |||
| | |||
| | |||
|Quadrantal angles | |||
| | |||
| | |||
|[[चतुर्थाँशीय कोण]] | |||
|- | |- | ||
| | | | ||
| | | | ||
| | |Trigonometric identities | ||
| | |||
| | | | ||
|त्रिकोणमितीय | |[[त्रिकोणमितीय सर्वसमिकाएँ]] | ||
|- | |- | ||
| | | | ||
| | | | ||
| | |Prinicipal solutions | ||
| | | | ||
| | | | ||
|[[मुख्य हल]] | |||
|- | |- | ||
| | | | ||
| | | | ||
| | |General solution | ||
| | |||
| | | | ||
| | |[[व्यापक हल]] | ||
|- | |- | ||
| | |||
| | | | ||
| | | | ||
Line 135: | Line 453: | ||
|Principle of Mathematical Induction | |Principle of Mathematical Induction | ||
|Motivation | |Motivation | ||
| | |||
|गणितीय आगमन का सिद्धांत | |गणितीय आगमन का सिद्धांत | ||
|प्रेरणा | |[[प्रेरणा]] | ||
|- | |- | ||
| | | | ||
Line 142: | Line 461: | ||
|The Principle of Mathematical Induction | |The Principle of Mathematical Induction | ||
| | | | ||
|गणितीय आगमन का सिद्धांत | | | ||
|[[गणितीय आगमन का सिद्धांत]] | |||
|- | |||
| | |||
| | |||
|Conjecture | |||
| | |||
| | |||
|[[अनुमान(कंजेक्चर)]] | |||
|- | |||
| | |||
| | |||
|Inductive hypothesis | |||
| | |||
| | |||
|[[आगमन परिकल्पना]] | |||
|- | |- | ||
| | |||
| | | | ||
| | | | ||
Line 153: | Line 488: | ||
|Complex Numbers and Quadratic Equations | |Complex Numbers and Quadratic Equations | ||
|Complex Numbers | |Complex Numbers | ||
|Ramamurthy | |||
Mani | |||
|सम्मिश्र संख्याएँ और द्विघातीय समीकरण | |सम्मिश्र संख्याएँ और द्विघातीय समीकरण | ||
|सम्मिश्र संख्याएँ | |[[सम्मिश्र संख्याएँ]] | ||
|- | |- | ||
| | | | ||
| | | | ||
|Algebra of Complex Numbers | |Algebra of Complex Numbers | ||
|Ramamurthy | |||
Mani | |||
| | | | ||
|सम्मिश्र संख्याओं का बीजगणित | |[[सम्मिश्र संख्याओं का बीजगणित]] | ||
|- | |- | ||
| | | | ||
| | | | ||
|The Modulus and the Conjugate of a Complex Number | |The Modulus and the Conjugate of a Complex Number | ||
|Ramamurthy | |||
Mani | |||
| | | | ||
|सम्मिश्र संख्या का मापांक और संयुग्मी | |[[सम्मिश्र संख्या का मापांक और संयुग्मी]] | ||
|- | |- | ||
| | | | ||
| | | | ||
|Argand Plane and Polar Representation | |Argand Plane and Polar Representation | ||
|Ramamurthy | |||
Mani | |||
| | | | ||
| | |[[आर्गंड तल और ध्रुवीय निरूपण]] | ||
|- | |- | ||
| | | | ||
Line 178: | Line 521: | ||
|Quadratic Equations | |Quadratic Equations | ||
| | | | ||
|द्विघातीय समीकरण | | | ||
|[[द्विघातीय समीकरण]] | |||
|- | |||
| | |||
| | |||
|Linear equations | |||
| | |||
| | |||
|[[रैखिक समीकरण]] | |||
|- | |||
| | |||
| | |||
|Closure Law | |||
| | |||
| | |||
|[[संवरक नियम]] | |||
|- | |||
| | |||
| | |||
|Commutative Law | |||
| | |||
| | |||
|[[क्रम विनिमय नियम]] | |||
|- | |||
| | |||
| | |||
|Associative Law | |||
| | |||
| | |||
|[[साहचर्य नियम]] | |||
|- | |- | ||
| | |||
| | |||
|Additive Inverse | |||
|Ramamurthy | |||
Mani | |||
| | |||
|[[योगात्मक प्रतिलोम]] | |||
|- | |||
| | |||
| | |||
|Additive Identity | |||
|Ramamurthy | |||
Mani | |||
| | |||
|[[योगात्मक तत्समक]] | |||
|- | |||
| | |||
| | |||
|Multiplicative identity | |||
|Ramamurthy | |||
Mani | |||
| | |||
|[[गुणात्मक तत्समक]] | |||
|- | |||
| | |||
| | |||
|Multiplicative inverse | |||
|Ramamurthy | |||
Mani | |||
| | |||
|[[गुणात्मक प्रतिलोम]] | |||
|- | |||
| | |||
| | |||
|Complex plane | |||
| | |||
| | |||
|[[सम्मिश्र तल]] | |||
|- | |||
| | |||
| | |||
|Real axis | |||
| | |||
| | |||
|[[वास्तविक अक्ष]] | |||
|- | |||
| | |||
| | |||
|Imaginary axis | |||
| | |||
| | |||
|[[काल्पनिक अक्ष]] | |||
|- | |||
| | |||
| | |||
|Polar co-ordinates | |||
| | |||
| | |||
|[[ध्रुवीय निर्देशांक]] | |||
|- | |||
| | |||
| | |||
|Principal argument | |||
| | |||
| | |||
|[[मुख्य आयाम]] | |||
|- | |||
| | |||
| | | | ||
| | | | ||
Line 189: | Line 629: | ||
|Linear Inequalities | |Linear Inequalities | ||
|Inequalities | |Inequalities | ||
| | |||
|रैखिक असमिकाएँ | |रैखिक असमिकाएँ | ||
|असमिकाएँ | |[[असमिकाएँ]] | ||
|- | |- | ||
| | | | ||
Line 197: | Line 638: | ||
their Graphical Representation | their Graphical Representation | ||
| | | | ||
|एक चर राशि के रैखिक असमिकाओं का बीजगणितीय हल | | | ||
और उनका आलेखीय निरूपण | |[[एक चर राशि के रैखिक असमिकाओं का बीजगणितीय हल और उनका आलेखीय निरूपण]] | ||
|- | |- | ||
| | | | ||
Line 204: | Line 645: | ||
|Graphical Solution of Linear Inequalities in Two Variables | |Graphical Solution of Linear Inequalities in Two Variables | ||
| | | | ||
|दो चर राशियों के रैखिक असमिकाओं का आलेखीय हल | | | ||
|[[दो चर राशियों के रैखिक असमिकाओं का आलेखीय हल]] | |||
|- | |- | ||
| | | | ||
Line 210: | Line 652: | ||
|Solutions of System of Linear Inequalities in Two Variables | |Solutions of System of Linear Inequalities in Two Variables | ||
| | | | ||
|दो चर राशियों की असमिका निकाय का हल | | | ||
|[[दो चर राशियों की असमिका निकाय का हल]] | |||
|- | |- | ||
| | |||
| | |||
|Numerical inequalities | |||
| | |||
| | |||
|[[संख्यांक असमिकाएँ]] | |||
|- | |||
| | |||
| | |||
|Literal inequalities | |||
| | |||
| | |||
|[[शाब्दिक असमिकाएँ]] | |||
|- | |||
| | |||
| | |||
|Strict inequalities | |||
| | |||
| | |||
|[[सुनिश्चित असमिकाएँ]] | |||
|- | |||
| | |||
| | |||
|Linear inequalities | |||
| | |||
| | |||
|[[रैखिक असमिकाएँ]] | |||
|- | |||
| | |||
| | | | ||
| | | | ||
Line 221: | Line 693: | ||
|Permutations and Combinations | |Permutations and Combinations | ||
|Fundamental Principle of Counting | |Fundamental Principle of Counting | ||
| | |||
|क्रमचय और संचय | |क्रमचय और संचय | ||
|गणना का आधारभूत सिद्धांत | |[[गणना का आधारभूत सिद्धांत]] | ||
|- | |- | ||
| | | | ||
Line 228: | Line 701: | ||
|Permutations | |Permutations | ||
| | | | ||
|क्रमचय | | | ||
|[[क्रमचय]] | |||
|- | |- | ||
| | | | ||
Line 234: | Line 708: | ||
|Combinations | |Combinations | ||
| | | | ||
|संचय | | | ||
|[[संचय]] | |||
|- | |- | ||
| | |||
| | |||
|Multiplication principle | |||
| | |||
| | |||
|[[गुणन सिद्धांत]] | |||
|- | |||
| | |||
| | | | ||
| | | | ||
Line 245: | Line 728: | ||
|Binomial Theorem | |Binomial Theorem | ||
|Binomial Theorem for Positive Integral Indices | |Binomial Theorem for Positive Integral Indices | ||
| | |||
|द्विपद प्रमेय | |द्विपद प्रमेय | ||
|धन पूर्णांकों के लिए द्विपद प्रमेय | |[[धन पूर्णांकों के लिए द्विपद प्रमेय]] | ||
|- | |- | ||
| | | | ||
Line 252: | Line 736: | ||
|General and Middle Terms | |General and Middle Terms | ||
| | | | ||
|व्यापक एवं मध्य पद | | | ||
|[[व्यापक एवं मध्य पद]] | |||
|- | |- | ||
| | |||
| | |||
|Binomial theorem | |||
| | |||
| | |||
|[[द्विपद प्रमेय]] | |||
|- | |||
| | |||
| | |||
|Pascal's triangle | |||
| | |||
| | |||
|[[पास्कल त्रिभुज]] | |||
|- | |||
| | |||
| | | | ||
| | | | ||
Line 263: | Line 763: | ||
|Sequences and Series | |Sequences and Series | ||
|Sequences | |Sequences | ||
|Ramamurthy Mani | |||
|अनुक्रम तथा श्रेणी | |अनुक्रम तथा श्रेणी | ||
|अनुक्रम | |[[अनुक्रम]] | ||
|- | |- | ||
| | | | ||
| | | | ||
|Series | |Series | ||
|Ramamurthy | |||
Mani | |||
| | | | ||
|श्रेणी | |[[श्रेणी]] | ||
|- | |- | ||
| | | | ||
Line 276: | Line 779: | ||
|Arithmetic Progression(A.P) | |Arithmetic Progression(A.P) | ||
| | | | ||
|समांतर | | | ||
|[[समांतर श्रेढ़ी]] | |||
|- | |- | ||
| | | | ||
| | | | ||
|Geometric Progression(G.P) | |Geometric Progression(G.P) | ||
|Ramamurthy | |||
Mani | |||
| | | | ||
|गुणोत्तर | |[[गुणोत्तर श्रेढ़ी]] | ||
|- | |- | ||
| | | | ||
| | | | ||
|Relationship between A.M and G.M | |Relationship between A.M and G.M | ||
|Ramamurthy | |||
Mani | |||
| | | | ||
|समांतर माध्य | |[[समांतर माध्य और गुणोत्तर माध्य के बीच संबंध]] | ||
|- | |- | ||
| | | | ||
Line 294: | Line 802: | ||
|Sum to n terms of Special Series | |Sum to n terms of Special Series | ||
| | | | ||
|विशेष अनुक्रमों के n पदों का योगफल | | | ||
|[[विशेष अनुक्रमों के n पदों का योगफल]] | |||
|- | |- | ||
| | |||
| | |||
|Progressions | |||
| | |||
| | |||
|[[श्रेढ़ी]] | |||
|- | |||
| | |||
| | |||
|Terms | |||
| | |||
| | |||
|[[पद]] | |||
|- | |||
| | |||
| | |||
|General term | |||
| | |||
| | |||
|[[व्यापक पद]] | |||
|- | |||
| | |||
| | |||
|Finite Sequence | |||
| | |||
| | |||
|[[परिमित अनुक्रम]] | |||
|- | |||
| | |||
| | |||
|Infinite sequence | |||
| | |||
| | |||
|[[अपरिमित अनुक्रम]] | |||
|- | |||
| | |||
| | |||
|Fibonacci Sequence | |||
|Ramamurthy Mani | |||
| | |||
|[[फिबोनाची अनुक्रम]] | |||
|- | |||
| | |||
| | |||
|Sigma Notation | |||
| | |||
| | |||
|[[सिग्मा संकेत]] | |||
|- | |||
| | |||
| | |||
|Arithmetic Mean | |||
| | |||
| | |||
|[[समांतर माध्य]] | |||
|- | |||
| | |||
| | |||
|Geometric Mean | |||
| | |||
| | |||
|[[गुणोत्तर माध्य]] | |||
|- | |||
| | |||
| | |||
|Common ratio | |||
| | |||
| | |||
|[[सार्व अनुपात]] | |||
|- | |||
| | |||
| | | | ||
| | | | ||
Line 305: | Line 885: | ||
|Straight Lines | |Straight Lines | ||
|Slope of a Line | |Slope of a Line | ||
| | |||
|सरल रेखाएं | |सरल रेखाएं | ||
|रेखा की ढाल | |[[रेखा की ढाल]] | ||
|- | |- | ||
| | | | ||
Line 312: | Line 893: | ||
|Various Forms of the Equations of a Line | |Various Forms of the Equations of a Line | ||
| | | | ||
|रेखा के समीकरणों के विविध रूप | | | ||
|[[रेखा के समीकरणों के विविध रूप]] | |||
|- | |- | ||
| | | | ||
Line 318: | Line 900: | ||
|General Equations of a Line | |General Equations of a Line | ||
| | | | ||
|रेखा का व्यापक समीकरण | | | ||
|[[रेखा का व्यापक समीकरण]] | |||
|- | |- | ||
| | | | ||
Line 324: | Line 907: | ||
|Distance of a Point from a Line | |Distance of a Point from a Line | ||
| | | | ||
|एक बिंदु की रेखा से दूरी | | | ||
|[[एक बिंदु की रेखा से दूरी]] | |||
|- | |||
| | |||
| | |||
|Analytical Geometry | |||
| | |||
| | |||
|[[वैश्लेषिक ज्यामिति]] | |||
|- | |- | ||
| | |||
| | | | ||
| | | | ||
Line 335: | Line 927: | ||
|Conic Sections | |Conic Sections | ||
|Sections of a Cone | |Sections of a Cone | ||
| | |||
|शंकु परिच्छेद | |शंकु परिच्छेद | ||
|शंकु के परिच्छेद | |[[शंकु के परिच्छेद]] | ||
|- | |- | ||
| | | | ||
Line 342: | Line 935: | ||
|Circle | |Circle | ||
| | | | ||
|वृत्त | | | ||
|[[वृत्त]] | |||
|- | |- | ||
| | | | ||
Line 348: | Line 942: | ||
|Parabola | |Parabola | ||
| | | | ||
|परवलय | | | ||
|[[परवलय]] | |||
|- | |- | ||
| | | | ||
Line 354: | Line 949: | ||
|Ellipse | |Ellipse | ||
| | | | ||
|दीर्घवृत्त | | | ||
|[[दीर्घवृत्त]] | |||
|- | |- | ||
| | | | ||
Line 360: | Line 956: | ||
|Hyperbola | |Hyperbola | ||
| | | | ||
|अतिपरवलय | | | ||
|[[अतिपरवलय]] | |||
|- | |||
| | |||
| | |||
|Conic Sections | |||
| | |||
| | |||
|[[शंकु परिच्छेद]] | |||
|- | |||
| | |||
| | |||
|Latus rectum | |||
| | |||
| | |||
|[[नाभिलंब जीवा]] | |||
|- | |||
| | |||
| | |||
|Eccentricity | |||
| | |||
| | |||
|[[उत्केन्द्रता]] | |||
|- | |- | ||
| | |||
| | | | ||
| | | | ||
Line 371: | Line 990: | ||
|Introduction to Three Dimensional Geometry | |Introduction to Three Dimensional Geometry | ||
|Coordinate Axes and Coordinate Planes in Three Dimensional Space | |Coordinate Axes and Coordinate Planes in Three Dimensional Space | ||
| | |||
|त्रिविमीय ज्यामिति का परिचय | |त्रिविमीय ज्यामिति का परिचय | ||
|त्रिविमीय अंतरिक्ष में निर्देशांक्ष और निर्देशांक-तल | |[[त्रिविमीय अंतरिक्ष में निर्देशांक्ष और निर्देशांक-तल]] | ||
|- | |- | ||
| | | | ||
| | | | ||
| | |Coordinates of a Point in Space | ||
| | |||
| | | | ||
|अंतरिक्ष में एक बिन्दु के निर्देशांक | |[[अंतरिक्ष में एक बिन्दु के निर्देशांक]] | ||
|- | |- | ||
| | | | ||
Line 384: | Line 1,005: | ||
|Distance between Two Points | |Distance between Two Points | ||
| | | | ||
|दो बिंदुओं के बीच की दूरी | | | ||
|[[दो बिंदुओं के बीच की दूरी]] | |||
|- | |- | ||
| | | | ||
Line 390: | Line 1,012: | ||
|Section Formula | |Section Formula | ||
| | | | ||
|विभाजन सूत्र | | | ||
|[[विभाजन सूत्र]] | |||
|- | |- | ||
| | |||
| | | | ||
| | | | ||
Line 402: | Line 1,026: | ||
|Intuitive Idea of Derivatives | |Intuitive Idea of Derivatives | ||
| | | | ||
| | |सीमा और अवकलज | ||
|[[अवकलाजों का सहजानुभूत बोध]] | |||
|- | |- | ||
| | | | ||
Line 409: | Line 1,034: | ||
| | | | ||
| | | | ||
|[[सीमाएं]] | |||
|- | |- | ||
| | | | ||
| | | | ||
|Limits of | |Limits of Trigonometric Functions | ||
| | | | ||
| | | | ||
|[[त्रिकोणमितीय फलनों की सीमाएं]] | |||
|- | |- | ||
| | | | ||
Line 421: | Line 1,048: | ||
| | | | ||
| | | | ||
|[[अवकलज]] | |||
|- | |||
| | |||
| | |||
|Calculus | |||
| | |||
| | |||
|[[कलन]] | |||
|- | |||
| | |||
| | |||
| | |||
| | |||
| | |||
| | |||
|- | |||
|14 | |||
|Mathematical Reasoning | |||
|Statements | |||
| | |||
|गणितीय विवेचन | |||
|[[कथन]] | |||
|- | |||
| | |||
| | |||
|New statements from Old | |||
| | |||
| | |||
|[[पूर्व ज्ञात कथनों से नए कथन बनाना]] | |||
|- | |||
| | |||
| | |||
|Special Words/Phrases | |||
| | |||
| | |||
|[[विशेष शब्द/वाक्यांश]] | |||
|- | |||
| | |||
| | |||
|Implications | |||
| | |||
| | |||
|[[अंतर्भाव]] | |||
|- | |||
| | |||
| | |||
|Validating Statements | |||
| | |||
| | |||
|[[कथनों की वैधता को प्रमाणित(सत्यापित) करना]] | |||
|- | |||
| | |||
| | |||
| | |||
| | |||
| | |||
| | |||
|- | |||
|15 | |||
|Statistics | |||
|Measures of Dispersion | |||
| | |||
|सांख्यिकी | |||
|[[प्रकीर्णन की माप]] | |||
|- | |||
| | |||
| | |||
|Range | |||
| | |||
| | |||
|[[परिसर]] | |||
|- | |||
| | |||
| | |||
|Mean Deviation | |||
| | |||
| | |||
|[[माध्य विचलन]] | |||
|- | |||
| | |||
| | |||
|Variance and Standard Deviation | |||
| | |||
| | |||
|[[प्रसरण और मानक विचलन]] | |||
|- | |||
| | |||
| | |||
|Analysis of Frequency Distributions | |||
| | |||
| | |||
|[[बारंबारता बंटनों का विश्लेषण]] | |||
|- | |||
| | |||
| | |||
|Continuous frequency distribution | |||
| | |||
| | |||
|[[सतत बारंबारता बंटन]] | |||
|- | |||
| | |||
| | |||
|Statistics | |||
| | |||
| | |||
|[[सांख्यिकी]] | |||
|- | |||
| | |||
| | |||
|Measure of Central Tendency | |||
| | |||
| | |||
|[[केन्द्रीय प्रवृत्ति की माप]] | |||
|- | |||
| | |||
| | |||
|Mean | |||
| | |||
| | |||
|[[माध्य]] | |||
|- | |||
| | |||
| | |||
|Mode | |||
| | |||
| | |||
|[[बहुलक]] | |||
|- | |||
| | |||
| | |||
|Median | |||
| | |||
| | |||
|[[माध्यिका]] | |||
|- | |||
| | |||
| | |||
|Quartile Deviation | |||
| | |||
| | |||
|[[चतुर्थक विचलन]] | |||
|- | |||
| | |||
| | |||
|Coefficient of variation | |||
| | |||
| | |||
|[[विचरण गुणांक]] | |||
|- | |||
| | |||
| | |||
| | |||
| | |||
| | |||
| | |||
|- | |||
|16 | |||
|Probability | |||
|Random Experiments | |||
| | |||
|प्रायिकता | |||
|[[यादृच्छिक परीक्षण]] | |||
|- | |||
| | |||
| | |||
|Event | |||
| | |||
| | |||
|[[घटना(प्रायिकता)]] | |||
|- | |||
| | |||
| | |||
|Axiomatic Approach to Probability | |||
| | |||
| | |||
|[[प्रायिकता की अभिगृहतीय दृष्टिकोण]] | |||
|- | |||
| | |||
| | |||
|Classical theory of probability | |||
| | |||
| | |||
|[[प्रायिकता का पुरातन सिद्धांत]] | |||
|- | |||
| | |||
| | |||
|Statistical approach of probability | |||
| | |||
| | |||
|[[प्रायिकता का सांख्यिकीय दृष्टिकोण]] | |||
|- | |||
| | |||
| | |||
|Outcome | |||
| | |||
| | |||
|[[संभावित परिणाम]] | |||
|- | |||
| | |||
| | |||
|Sample space | |||
| | |||
| | |||
|[[प्रतिदर्श समष्टि]] | |||
|- | |||
| | |||
| | |||
|Sample Points | |||
| | |||
| | |||
|[[प्रतिदर्श बिंदुओं]] | |||
|- | |||
| | |||
| | |||
|Impossible Event | |||
| | |||
| | |||
|[[असंभव घटना]] | |||
|- | |||
| | |||
| | |||
|Sure Event | |||
| | |||
| | |||
|[[निश्चित घटना]] | |||
|- | |||
| | |||
| | |||
|Simple Event | |||
|Ramamurthy | |||
Mani | |||
| | |||
|[[सरल घटना]] | |||
|- | |||
| | |||
| | |||
|Compound Event | |||
|Ramamurthy | |||
Mani | |||
| | |||
|[[मिश्र घटना]] | |||
|- | |||
| | |||
| | |||
|Complementary Event | |||
| | |||
| | |||
|[[पूरक घटना]] | |||
|- | |||
| | |||
| | |||
|Mutually exclusive events | |||
| | |||
| | |||
|[[परस्पर अपवर्जी घटनाएँ]] | |||
|- | |||
| | |||
| | |||
|Exhaustive events | |||
| | |||
| | |||
|[[निःशेष घटनाएँ]] | |||
|- | |||
| | |||
| | |||
|Probability of an event | |||
| | |||
| | |||
|[[घटना की प्रायिकता]] | |||
|- | |||
| | |||
| | |||
| | |||
| | |||
| | |||
| | |||
|- | |||
|17 | |||
|Infinite Series | |||
| | |||
| | |||
|अनंत श्रेणी | |||
| | |||
|- | |||
| | |||
|Appendix-1 | |||
|Binomial Theorem for any Index | |||
| | |||
| | |||
|[[किसी घातांक के लिए द्विपद प्रमेय]] | |||
|- | |||
| | |||
| | |||
|Infinite Geometric Series | |||
| | |||
| | |||
|[[अनंत गुणोत्तर श्रेणी]] | |||
|- | |||
| | |||
| | |||
|Exponential series | |||
| | |||
| | |||
|[[चरघातांकी श्रेणी]] | |||
|- | |||
| | |||
| | |||
|Logarithmic series | |||
| | |||
| | |||
|[[लघुगणकीय श्रेणी]] | |||
|- | |||
| | |||
| | |||
|Infinite Series | |||
| | |||
| | |||
|[[अनंत श्रेणी]] | |||
|- | |||
| | |||
| | |||
|Infinite Sequence | |||
| | |||
| | |||
|[[अनंत अनुक्रम]] | |||
|- | |||
| | |||
| | |||
|Binomial Series | |||
| | |||
| | |||
|[[द्विपद श्रेणी]] | |||
|- | |||
| | |||
| | |||
| | |||
| | |||
| | |||
| | |||
|- | |||
| | |||
|Appendix-2 | |||
|Preliminaries | |||
| | |||
| | |||
|[[प्रारंभिक प्रबंध]] | |||
|- | |||
| | |||
| | |||
|What is Mathematical Modelling | |||
| | |||
| | |||
|[[गणितीय निदर्शन क्या है]] | |||
|- | |||
| | |||
| | |||
|Mathematical Modelling | |||
| | |||
| | |||
|[[गणितीय निदर्शन]] | |||
|- | |||
| | |||
| | |||
|Interpretation of the model | |||
| | |||
| | |||
|[[निदर्श का अर्थ निर्वचन]] | |||
|- | |||
| | |||
| | |||
|Validation of the model | |||
| | |||
| | |||
|[[निदर्श का मान्यकरण]] | |||
|- | |||
| | |||
| | |||
|Solution of the model | |||
| | |||
| | |||
|[[निदर्श का हल]] | |||
|} | |} | ||
[[Category:Information]] |
Latest revision as of 17:39, 17 April 2024
S.No | Chapters | Topics | Article Creator Name | अध्याय | विषय |
---|---|---|---|---|---|
1 | Sets | Sets and their representations | Ramamurthy
Mani |
समुच्चय | समुच्चय और उनका निरूपण |
The Empty Set/Void Set | Ramamurthy
Mani |
रिक्त समुच्चय | |||
Finite and Infinite Sets | Ramamurthy
Mani |
परिमित और अपरिमित समुच्चय | |||
Equal Sets | Ramamurthy
Mani |
समान समुच्चय | |||
Subsets | उपसमुच्चय | ||||
Power Set | Ramamurthy
Mani |
घात समुच्चय | |||
Universal Set | Ramamurthy
Mani |
सार्वत्रिक समुच्चय | |||
Venn Diagrams | Ramamurthy
Mani |
वेन आरेख | |||
Operations on Sets | Ramamurthy
Mani |
समुच्चयों पर संक्रियाएँ | |||
Complement of a Set | समुच्चय का पूरक | ||||
Practical Problems on Union and Intersection of Two Sets | दो समुच्चयों के सम्मिलन और सर्वनिष्ठ पर आधारित व्यावहारिक प्रश्न | ||||
Sets | समुच्चय | ||||
Geometry | ज्यामिति | ||||
Sequences | अनुक्रम | ||||
Probability | प्रायिकता | ||||
Trigonometric series | त्रिकोणमितीय श्रेणी | ||||
Natural Numbers | प्राकृत संख्याएँ | ||||
Prime Numbers | अभाज्य संख्याएँ | ||||
Triangles | त्रिभुज | ||||
Prime factors | अभाज्य गुणनखंड | ||||
Equation | समीकरण | ||||
Integers | पूर्णांक | ||||
Rational Numbers | परिमेय संख्याएँ | ||||
Real Numbers | वास्तविक संख्याएँ | ||||
Roster or tabular form (Sets) | रोस्टर या सारणीबद्ध रूप (समुच्चय) | ||||
Set-builder form (Sets) | समुच्चय-निर्माण रूप(समुच्चय) | ||||
Null Set | शून्य समुच्चय | ||||
Superset | अधिसमुच्चय | ||||
Singleton set | एकल समुच्चय | ||||
Closed Interval | संवृत(बंद) अंतराल | ||||
Open Interval | खुला अंतराल | ||||
Union (sets) | सम्मिलन(समुच्चय) | ||||
Intersection (sets) | सर्वनिष्ट(समुच्चय) | ||||
Disjoint Sets | असंयुक्त समुच्चय | ||||
2 | Relations and Functions | Cartesian Product of Sets | संबंध और फलन | समुच्चयों का कार्टेशियन गुणन | |
Relations | संबंध | ||||
Functions | फलन | ||||
Ordered triplet | क्रमित त्रिक | ||||
Domain (sets) | प्रांत(समुच्चय) | ||||
Range (Sets) | परिसर(समुच्चय) | ||||
Arrow diagram (Sets) | दृष्टि चित्रण(समुच्चय) | ||||
Codomain (Sets) | सहप्रांत(समुच्चय) | ||||
Real Function | वास्तविक फलन | ||||
Identity function (sets) | तत्समक फलन(समुच्चय) | ||||
Constant function (sets) | अचर फलन(समुच्चय) | ||||
Polynomial functions (sets) | बहुपदीय फलन(समुच्चय) | ||||
Rational functions (sets) | परिमेय फलन(समुच्चय) | ||||
Modulus function (sets) | मापांक फलन(समुच्चय) | ||||
Signum function (sets) | चिन्ह फलन(समुच्चय) | ||||
Greatest integer function (sets) | महत्तम पूर्णांक फलन(समुच्चय) | ||||
3 | Trignometric Functions | Angles | Ramamurthy
Mani |
त्रिकोणमितीय फलन | कोण |
Trigonometric Functions | त्रिकोणमितीय फलन | ||||
Trigonometric Functions of Sum and Difference of Two Angles | दो कोणों के योग और अंतर का त्रिकोणमितीय फलन | ||||
Trigonometric Equations | त्रिकोणमितीय समीकरण | ||||
Trigonometry | त्रिकोणमिति | ||||
Quadrantal angles | चतुर्थाँशीय कोण | ||||
Trigonometric identities | त्रिकोणमितीय सर्वसमिकाएँ | ||||
Prinicipal solutions | मुख्य हल | ||||
General solution | व्यापक हल | ||||
4 | Principle of Mathematical Induction | Motivation | गणितीय आगमन का सिद्धांत | प्रेरणा | |
The Principle of Mathematical Induction | गणितीय आगमन का सिद्धांत | ||||
Conjecture | अनुमान(कंजेक्चर) | ||||
Inductive hypothesis | आगमन परिकल्पना | ||||
5 | Complex Numbers and Quadratic Equations | Complex Numbers | Ramamurthy
Mani |
सम्मिश्र संख्याएँ और द्विघातीय समीकरण | सम्मिश्र संख्याएँ |
Algebra of Complex Numbers | Ramamurthy
Mani |
सम्मिश्र संख्याओं का बीजगणित | |||
The Modulus and the Conjugate of a Complex Number | Ramamurthy
Mani |
सम्मिश्र संख्या का मापांक और संयुग्मी | |||
Argand Plane and Polar Representation | Ramamurthy
Mani |
आर्गंड तल और ध्रुवीय निरूपण | |||
Quadratic Equations | द्विघातीय समीकरण | ||||
Linear equations | रैखिक समीकरण | ||||
Closure Law | संवरक नियम | ||||
Commutative Law | क्रम विनिमय नियम | ||||
Associative Law | साहचर्य नियम | ||||
Additive Inverse | Ramamurthy
Mani |
योगात्मक प्रतिलोम | |||
Additive Identity | Ramamurthy
Mani |
योगात्मक तत्समक | |||
Multiplicative identity | Ramamurthy
Mani |
गुणात्मक तत्समक | |||
Multiplicative inverse | Ramamurthy
Mani |
गुणात्मक प्रतिलोम | |||
Complex plane | सम्मिश्र तल | ||||
Real axis | वास्तविक अक्ष | ||||
Imaginary axis | काल्पनिक अक्ष | ||||
Polar co-ordinates | ध्रुवीय निर्देशांक | ||||
Principal argument | मुख्य आयाम | ||||
6 | Linear Inequalities | Inequalities | रैखिक असमिकाएँ | असमिकाएँ | |
Algebraic Solutions of Linear Inequalities in One Variable and
their Graphical Representation |
एक चर राशि के रैखिक असमिकाओं का बीजगणितीय हल और उनका आलेखीय निरूपण | ||||
Graphical Solution of Linear Inequalities in Two Variables | दो चर राशियों के रैखिक असमिकाओं का आलेखीय हल | ||||
Solutions of System of Linear Inequalities in Two Variables | दो चर राशियों की असमिका निकाय का हल | ||||
Numerical inequalities | संख्यांक असमिकाएँ | ||||
Literal inequalities | शाब्दिक असमिकाएँ | ||||
Strict inequalities | सुनिश्चित असमिकाएँ | ||||
Linear inequalities | रैखिक असमिकाएँ | ||||
7 | Permutations and Combinations | Fundamental Principle of Counting | क्रमचय और संचय | गणना का आधारभूत सिद्धांत | |
Permutations | क्रमचय | ||||
Combinations | संचय | ||||
Multiplication principle | गुणन सिद्धांत | ||||
8 | Binomial Theorem | Binomial Theorem for Positive Integral Indices | द्विपद प्रमेय | धन पूर्णांकों के लिए द्विपद प्रमेय | |
General and Middle Terms | व्यापक एवं मध्य पद | ||||
Binomial theorem | द्विपद प्रमेय | ||||
Pascal's triangle | पास्कल त्रिभुज | ||||
9 | Sequences and Series | Sequences | Ramamurthy Mani | अनुक्रम तथा श्रेणी | अनुक्रम |
Series | Ramamurthy
Mani |
श्रेणी | |||
Arithmetic Progression(A.P) | समांतर श्रेढ़ी | ||||
Geometric Progression(G.P) | Ramamurthy
Mani |
गुणोत्तर श्रेढ़ी | |||
Relationship between A.M and G.M | Ramamurthy
Mani |
समांतर माध्य और गुणोत्तर माध्य के बीच संबंध | |||
Sum to n terms of Special Series | विशेष अनुक्रमों के n पदों का योगफल | ||||
Progressions | श्रेढ़ी | ||||
Terms | पद | ||||
General term | व्यापक पद | ||||
Finite Sequence | परिमित अनुक्रम | ||||
Infinite sequence | अपरिमित अनुक्रम | ||||
Fibonacci Sequence | Ramamurthy Mani | फिबोनाची अनुक्रम | |||
Sigma Notation | सिग्मा संकेत | ||||
Arithmetic Mean | समांतर माध्य | ||||
Geometric Mean | गुणोत्तर माध्य | ||||
Common ratio | सार्व अनुपात | ||||
10 | Straight Lines | Slope of a Line | सरल रेखाएं | रेखा की ढाल | |
Various Forms of the Equations of a Line | रेखा के समीकरणों के विविध रूप | ||||
General Equations of a Line | रेखा का व्यापक समीकरण | ||||
Distance of a Point from a Line | एक बिंदु की रेखा से दूरी | ||||
Analytical Geometry | वैश्लेषिक ज्यामिति | ||||
11 | Conic Sections | Sections of a Cone | शंकु परिच्छेद | शंकु के परिच्छेद | |
Circle | वृत्त | ||||
Parabola | परवलय | ||||
Ellipse | दीर्घवृत्त | ||||
Hyperbola | अतिपरवलय | ||||
Conic Sections | शंकु परिच्छेद | ||||
Latus rectum | नाभिलंब जीवा | ||||
Eccentricity | उत्केन्द्रता | ||||
12 | Introduction to Three Dimensional Geometry | Coordinate Axes and Coordinate Planes in Three Dimensional Space | त्रिविमीय ज्यामिति का परिचय | त्रिविमीय अंतरिक्ष में निर्देशांक्ष और निर्देशांक-तल | |
Coordinates of a Point in Space | अंतरिक्ष में एक बिन्दु के निर्देशांक | ||||
Distance between Two Points | दो बिंदुओं के बीच की दूरी | ||||
Section Formula | विभाजन सूत्र | ||||
13 | Limits and Derivatives | Intuitive Idea of Derivatives | सीमा और अवकलज | अवकलाजों का सहजानुभूत बोध | |
Limits | सीमाएं | ||||
Limits of Trigonometric Functions | त्रिकोणमितीय फलनों की सीमाएं | ||||
Derivatives | अवकलज | ||||
Calculus | कलन | ||||
14 | Mathematical Reasoning | Statements | गणितीय विवेचन | कथन | |
New statements from Old | पूर्व ज्ञात कथनों से नए कथन बनाना | ||||
Special Words/Phrases | विशेष शब्द/वाक्यांश | ||||
Implications | अंतर्भाव | ||||
Validating Statements | कथनों की वैधता को प्रमाणित(सत्यापित) करना | ||||
15 | Statistics | Measures of Dispersion | सांख्यिकी | प्रकीर्णन की माप | |
Range | परिसर | ||||
Mean Deviation | माध्य विचलन | ||||
Variance and Standard Deviation | प्रसरण और मानक विचलन | ||||
Analysis of Frequency Distributions | बारंबारता बंटनों का विश्लेषण | ||||
Continuous frequency distribution | सतत बारंबारता बंटन | ||||
Statistics | सांख्यिकी | ||||
Measure of Central Tendency | केन्द्रीय प्रवृत्ति की माप | ||||
Mean | माध्य | ||||
Mode | बहुलक | ||||
Median | माध्यिका | ||||
Quartile Deviation | चतुर्थक विचलन | ||||
Coefficient of variation | विचरण गुणांक | ||||
16 | Probability | Random Experiments | प्रायिकता | यादृच्छिक परीक्षण | |
Event | घटना(प्रायिकता) | ||||
Axiomatic Approach to Probability | प्रायिकता की अभिगृहतीय दृष्टिकोण | ||||
Classical theory of probability | प्रायिकता का पुरातन सिद्धांत | ||||
Statistical approach of probability | प्रायिकता का सांख्यिकीय दृष्टिकोण | ||||
Outcome | संभावित परिणाम | ||||
Sample space | प्रतिदर्श समष्टि | ||||
Sample Points | प्रतिदर्श बिंदुओं | ||||
Impossible Event | असंभव घटना | ||||
Sure Event | निश्चित घटना | ||||
Simple Event | Ramamurthy
Mani |
सरल घटना | |||
Compound Event | Ramamurthy
Mani |
मिश्र घटना | |||
Complementary Event | पूरक घटना | ||||
Mutually exclusive events | परस्पर अपवर्जी घटनाएँ | ||||
Exhaustive events | निःशेष घटनाएँ | ||||
Probability of an event | घटना की प्रायिकता | ||||
17 | Infinite Series | अनंत श्रेणी | |||
Appendix-1 | Binomial Theorem for any Index | किसी घातांक के लिए द्विपद प्रमेय | |||
Infinite Geometric Series | अनंत गुणोत्तर श्रेणी | ||||
Exponential series | चरघातांकी श्रेणी | ||||
Logarithmic series | लघुगणकीय श्रेणी | ||||
Infinite Series | अनंत श्रेणी | ||||
Infinite Sequence | अनंत अनुक्रम | ||||
Binomial Series | द्विपद श्रेणी | ||||
Appendix-2 | Preliminaries | प्रारंभिक प्रबंध | |||
What is Mathematical Modelling | गणितीय निदर्शन क्या है | ||||
Mathematical Modelling | गणितीय निदर्शन | ||||
Interpretation of the model | निदर्श का अर्थ निर्वचन | ||||
Validation of the model | निदर्श का मान्यकरण | ||||
Solution of the model | निदर्श का हल |